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As a section of an workout program to toughen their pectoral muscles a person stretches a spring which has a spring constant k = 520 N/m. Write an equation for the work necessary to stretch the spring from the relaxed state to a distance x1.

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To develop the problem it is necessary to apply the concepts related to Hooke's Law. For which it is understood that

[tex]F = kx[/tex]

Where,

k = Spring constant

x = Displacement of Spring

By the theorem of work we understand that it is the force realized when there is the path of an object therefore

[tex]dW =Fdx[/tex]

Our value of F is

[tex]dW = (kx)dx[/tex]

Integrating

[tex]W = k\int\limit_0^{x_1} xdx[/tex]

Therefore the expresion is

[tex]W = \frac{kx_1^2}{2}[/tex]

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